As a conventional high-speed positioning mechanism for a tool, there has been the one that directly moves a tool stand in one-axial direction by a piezoelectric element, a voice coil motor and an electromagnetic force (“Study on In-process Recognition of Machining Mode in Micro-cutting of Optical Glass”, Japan Society of Precision Engineering Journal, Vol. 67, No. 5, 2001, p. 844 to 849). FIG. 17 shows an internal structural diagram of the conventional high-speed positioning mechanism.
As shown in FIG. 17, the conventional high-speed positioning mechanism has the structure in which a cylindrical piezoelectric element 101 is fitted in a casing 100, and a tool holder 102 which is a movable part is supported by a diaphragm 103 so that the displacement of the tool holder 102 is directly measured by a capacity type displacement sensor 104. The tool holder 102, the capacity type displacement sensor 104 and a diamond tool 105 are disposed so that center lines of them are aligned with each other.
FIG. 18 shows a block diagram of a position control loop circuit that performs positioning control of the tool in the above described conventional high-speed positioning mechanism. The conventional high-speed positioning mechanism feeds back a signal indicating a displacement amount of the tool holder 102 by the capacity type displacement sensor 104, phase-compensates a deviation of the fed-back signal and a command value by a compensation circuit including an integrator 110 and a notch filter 111, performs power amplification of the phase-compensated signal by an amplifier (included in a block 112) to perform positional control of the cylindrical piezoelectric element 101.
In recent years, with the developments in an optical design technique and machining technique, a nonaxisymmetric aspheric surface (commonly called “free curved surface” sometimes since the nonaxisymmetric aspheric surface is not rotationally symmetric and has no symmetrical surface in any quadrant) has been achieved.
For machining to make a surface to be machined a nonaxisymmetric aspheric surface, a machining method called a raster fly cut method is used. FIG. 19 shows a schematic view of the raster fly cut method. In this machining method, a workpiece 202 is slowly machined for each line as raster scanning based on NC data by a tool 201 attached to a shaft 200 rotating at a high speed. When machining for one line is finished, the tool 201 is returned to the original position, and by shifting the pitch by a predetermined distance, the next line is machined. In short, the surface to be machined is finished by one-way machining. This is because reciprocating machining makes the machined surface on which up-cut surfaces and down-cut surfaces are alternately repeated, and the state of the machined surface is not constant. Therefore, reciprocating machining is not used for finish machining, though it is sometimes used in rough machining. In addition, reciprocating machining is not desirable in terms of the wear of tools. For the above reasons, one-way machining is generally used in the raster fly cut method.
This raster fly cut method has relatively less restriction, and this method can be realized by only attaching a tool via a holder to the shaft rotating at a high speed on an ultra-precision processing machine which triaxially operates. However, the largest disadvantage of this machining method is that it requires a long machining time. In the case of finishing a nonaxisymmetric aspheric surface of, for example, approximately 200 mm×10 mm, the machining time of substantially 20 hours is required. When the machining takes such a long time, machining accuracy is reduced. In other words, the machining environment (temperature, atmospheric pressure, humidity, disturbance such as vibration, and the like) is highly likely to change during machining, and the change in the machining environment is the factor of preventing the accuracy from being improved. Tremendous cost is required to reduce the factor of these environmental changes with relatively small effects. In addition, in this machining method, the time and the volume of the data required for creating the NC data are tremendous.
Thus, it is conceivable that the above described high-speed positioning mechanism of one uniaxial constitution is also used even in machining for making the surface to be machined a nonaxisymmetric aspheric surface. In the case of using this mechanism, the workpiece is rotated as if the workpiece were machined with a lathe, and the tool is moved in the radius direction of rotation of the workpiece while the tool is being controlled at a high speed. If this machining can be realized, there arises the possibility of making the machining time equal to the time required for machining to make the surface to be machined a rotational symmetrical surface. That is, the machining time can be shortened to approximately 1/10 to 1/100 as compared with the machining time by the conventional raster fly cut method.
However, the above described high-speed positioning mechanism of the uniaxial constitution has the disadvantage that rigidity in the direction orthogonal to the operating direction of the movable shaft is low. In the constitution example shown in FIG. 17, the portion in the direction orthogonal to the operating direction of the movable shaft is supported by only the diaphragm 103. Even if the tool is held by such a supporting method, a favorable machined surface is not achieved since the rigidity in the direction orthogonal to the operating direction of the movable shaft is low and the tool needlessly moves due to the machining resistance.
In addition, when machining is performed by using the above described high-speed positioning mechanism of the uniaxial constitution, the cutting edge of the tool is limited in size, and therefore, it is necessary to in advance calculate with which portion of the cutting edge the work piece is machined, and control the position of the tool. This problem is explained with reference to FIG. 20.
FIG. 20 shows an explanatory diagram for explaining the machining operation of the conventional high-speed positioning mechanism of the uniaxial constitution. Herein, in order to facilitate understanding of the above described problem of the high-speed positioning mechanism of the uniaxial constitution, an explanation will be made by illustrating machining for creating the rotational symmetrical surface defined by the function z=f(x) as an example.
The high-speed positioning mechanism of the uniaxial constitution operates a tool 300 in only a Z-axis direction. The tool 300 has a cutting edge of a constant radius r. The workpiece is rotated around the Z axis. In this example, machining to be performed on an axially symmetrical surface is adopted, and therefore, the high-speed positioning mechanism of the uniaxial constitution is moved toward the rotational center from the outer peripheral side of the rotating workpiece.
When an arbitrary point (control point) P on the curved surface defined by the function z=f(x) is finished as shown in FIG. 20, the high-speed positioning mechanism of the uniaxial constitution drives the tool 300 so that a tip end portion of the cutting edge of the tool 300 coincides with the control point P, but at this time, a portion different from the tip end portion of the cutting edge contacts the already machined portion of the workpiece, and an interference point (actual machining point) M which the cutting edge interferes with and the control point P do not coincide with each other. As a result, the workpiece is excessively cut from the curved surface defined by the function z=f(x), and a favorable machined surface is not achieved.
In order to avoid the problem of excessive cutting, it is preferable if the interference point can be calculated in real time during machining, but in view of the actual machining speed, and calculation ability of a computer, it is difficult with the current technology. Therefore, it is necessary to calculate in advance the position where the tool should trace, before starting the machining operation, and to perform machining based on the NC data. When the rotational symmetrical surface as shown in FIG. 20 is produced, the calculation amount is small, and much time and effort are not required. However, when a nonaxisymmetric aspheric surface which does not have a symmetrical shape is produced, the number of calculation points of the NC data reaches 1 million even when the nonaxisymmetric aspheric surface is a small surface 10 mm square, for example. Since convergent calculation accompanies calculation of the NC data though not described in detail, calculation time is tremendous with a large amount of calculation (Japanese Patent Laid-Open No. 2001-282332). It is not uncommon occurrence that the capacity of the produced NC data exceeds 100 megabytes. In actual machining, when the tool is replaced with the one having a different radius of the cutting edge, the NC data needs to be produced at each replacement.
In short, even if machining of producing a nonaxisymmetric aspheric surface can be realized by the conventional high-speed positioning mechanism of the uniaxial constitution, an immense amount of time is required for creation of the NC data though the machining time is shortened, and this is not practical with all the factors considered. Therefore, such a method has not been practically used conventionally.